Fanography

A tool to visually study the geography of Fano 3-folds.

del Pezzo surface: $\mathrm{Bl}_3\mathbb{P}^2$

Identification

del Pezzo surface $\mathrm{Bl}_3\mathbb{P}^2$
Picard rank
4
$-\mathrm{K}_S^2$
6
Hodge diamond
1
0 0
0 4 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(S,\omega_S^\vee)$
7
$-\mathrm{K}_S$ very ample?
yes
Deformation theory
number of moduli
0
Automorphism groups
group dimension
$(\mathbb{G}_{\mathrm{m}}^2\rtimes\mathrm{Sym}_3)\times\mathrm{Sym}_2$ 2